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1 INTRODUCTION

Offshore Infrastructure located on Polish Southern

Baltic Sea have a long history, beginning in the 1960s as

“Petrobaltic” for oil and gas exploration activities,

intensified in May 1992 when production phase has

been start. From the outset this infrastructure mostly

based on jack-up platforms originally designed for

different site conditions [26]. Chartering or purchasing

jack-up to operate in basin other than those for which

they were designed is a common practice. However

many factors that have to be taken into consideration

beside the standardised site assessment that impact on

reliability of jack-up platform [3], [4], [21]. Especially

when the design life expectancy is exceeded and

lifetime extension plan is not only consider but already

introduced by special survey and maintenance or even

upgrades. Not only on Southern Baltic Sea, but in

general platforms exceeding typical design lifetime are

still in operation. In these circumstances the proper

lifetime analysis and assessment is crucial to provide

answer for how long particular platform can be still

safely operating. As it is not directly mentioned or

required by Site Specific Assessment according to ISO

19905-1, the proposed approach may be found helpful

by Classification Societies and companies performing a

comprehensive assessment that includes the history of

transit and jacking operations in order to establish the

overall state of the platform [19].

The problem of ageing of offshore structures with

their equipment including history of operation, the

risks that it brings and how is it related to overall

reliability of jack-up offshore platform is purpose of

this article study. Many papers refer to structural

reliability of offshore platforms and their lifetime

estimation by analysing their components fatigue [15],

[36]. Authors in reference [15] perform reliability

analysis of offshore platforms taking into account

fatigue degradation of components, and consider

The Impact of Operation History on Jack-up Structure

Reliability

A. Blokus-Dziula

& D. Dobrzański

Gdynia Maritime University, Gdynia, Poland

Global Maritime, Gdynia, Poland

ABSTRACT: In the Polish Baltic Sea region, jack-up structures, apart from existing offshore oil and gas offshore

infrastructure, will be used for further wind farm installation. These structures usually operate under various

environmental and geotechnical conditions, often in a different basin than they were designed for. Therefore, the

operation history is of great importance for fatigue and reliability assessment of jack-up structures. The article

first presents the construction and main components of jack-up structure, focusing on jacking system. Next, it

analyses how the frequency and conditions of transit and jacking operations may impact on overall fatigue of

jack-up structure and its components. In addition to time-dependent factors, such as corrosion and material

degradation, the operations’ history is also included in the research. The results illustrate that operational history

should not be neglect in safety analysis of subsequent operations, as well as in the planning of inspections and

maintenance.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 19

Number 4

December 2025

DOI: 10.12716/1001.19.04.38

1390

different failure scenarios, including various sequences

of failures and combinations of time sequences.

However in practice, many accidents are related to the

operation of platforms and additional circumstances

such as operational and environmental conditions.

According to Ibrion et al. [18] 96% of accidents

occurrence were related to operation, including 13% to

operation and installation, and only 4% to installation.

The rate of accidents linked to jack-up on Norwegian

Coastal Shelf for last 40 years is 1,25 which is not

significantly high in comparison to concrete structures

or jacket [18]. It should be emphasized that Southern

Baltic Sea have over-representation of jack-up type

platform, while concrete structures and jacket type of

foundation are most common worldwide. What is also

important, the majority of considered jack-up

platforms operate on field for long time without

change of operational site. This characteristic should be

carefully considered, as there is not clear how to

categorize and compare the reliability levels based on

global data.

2 JACK-UP PLATFORM AND ITS RELIABILITY

STRUCTURE

2.1 Jack-up unit description and components

In the Polish Baltic Sea area, apart from the existing oil

and gas offshore infrastructures based mostly on jack-

up platforms, vessels of the same type, i.e. jack-up, will

also be used for subsequent wind farm installation. In

the case of offshore wind farm installation vessels, a

similar assumption can be made as in the case of

drilling platforms. Namely, most of these vessels have

been operating in various waters, which is directly

related to the history of transit and jacking operations.

The frequency and conditions of these operations

impact on overall fatigue of jack-up structure and its

reliability. Consequently, it is important for the safety

of subsequent operations and can also be basis for

determining the scope of inspections, repairs, or

modifications to the vessel.

The construction of such offshore structures should

be analysed before further study. Jack-up units consist

of a buoyant hull equipped with multiple retractable

legs, typically three or four, capable of raising the hull

above the sea surface. For the purpose of this study

typical three-legged structure with a triangular hull is

presented in Figure 1.

Figure 1. Simplified 3-D model of typical three-legged jack-

up hull-leg assembly (based on [28] AI generated).

In general three-legged jack-up reliability structure

can be simplified to the scheme presented in Figure 2.

Figure 2. Simplified reliability structure of three-legged jack-

up.

In Figure 2, the notation LS is used for “leg

structure” that includes spud-can and jack house.

Further, the reliability structure of all three legs are

described and analysed depending on the platform

operation mode. Each leg structure is connected to the

hull, however for three-legged structure each of them

must be functional, so the jack-up structure has been

simplified to a series reliability structure. For other

jack-ups design, the reliability structure should be

redefined.

The concept of reliability has various definitions,

even within the offshore industry, and different

approaches to its assessment can be found. The

reliability term appears at many stages of offshore

projects and often refers to different issues [16]. In case

of offshore object, its reliability can be formulated as

the combined fulfilment of the requirements of

structural integrity and operational efficiency of

systems while maintaining a sufficient level of

serviceability, maintainability, availability and quality

that ensures the safety of people on board, the

environment and performs the designed function with

a reasonable degree of certainty.

In the literature review on jack-up reliability

analysis [10], the authors point out that results of

failure probability analysis largely depend on the

method used apart from factors included in the

reliability analysis. By applying different methods and

approaches to structural reliability analysis, the

authors conclude that their choice depends mainly on

the way of treating and understanding uncertainties in

reliability assessment. In reliability analysis, taking

into account deterioration and degradation of

structure/system and its components in time,

uncertainties can refer to various aspects. Future

studies on proposed in this article approach will focus

on methods to reduce these uncertainties.

Referring to the classical reliability theory of two-

state systems, the reliability is defined as the

probability or likelihood that the system will be failed

or damaged. Following this definition and considering

the probability of failure over time, the reliability

function of a system R(t), t ≥ 0, is defined [23] as the

probability that the time to system failure, i.e. its

lifetime, is not shorter than t:

( ) ( )

, 0,

R t P T t t=  

(1)

where TF denotes random variable representing the

system lifetime.

In the reliability analysis of offshore units, it is

crucial not only to determine their design lifetime and

the time period of system failure but also to estimate

the period during which the offshore unit can be safely

operated under specific conditions [2], [12]. This goal

can be achieved in various ways, taking into account

operating cycles and conditions data. For example, by

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determining the moment at which the unit’s reliability

is most likely to exceed a certain acceptable threshold,

beyond which operation may be unsafe. In that sense,

Jensen [20] estimates the average value of the expected

fatigue damage rate and the probability that the

expected fatigue damage rate D exceeds

predetermined threshold DT, by using the Cornell

reliability index β:

( ) ( )

Φ.

P D D



 = −

(2)

Cornell reliability index [9] is widely used in

literature to evaluate the reliability of offshore units

[10], [15], [22], [36]. Nevertheless, in this paper we

propose to use the reliability function to analyze the

reliability of offshore platforms, which allows to

consider the reliability value depending on the time

and operation mode of the platform. Moreover, a

multi-state approach to reliability analysis, described

in Subsection 2.3, is proposed to consider the

probability of platform being in a specific reliability

state. Such reliability state can correspond to the

offshore unit condition, including fatigue level of its

structure and main components, related to its

operational history.

Consequently, we apply the formula (1), to evaluate

the reliability of jack-up unit. Considering reliability

structure of a three-legged jack-up platform, we

conclude that it is working when all its main

subsystems (platform legs and connected equipment)

and the hull are functional for designated task

(operation mode). Thus, a basic reliability structure of

platform is a series reliability structure, presented in

Figure 2. The remaining components have been

omitted in the reliability structure due to their

negligible influence on the platform reliability in the

considered scope, i.e., maintaining the pontoon

structure in a specific position or not contributing to

the operating mode. We focus on mechanical integrity

and omit other equally important platform functions

for simplicity, to demonstrate the motivation behind

the proposed approach, which could be expanded to

include additional functionalities in the future.

Taking into account the above conclusion, the

reliability function of jack-up system is given by the

following formula:

( ) ( ) ( ) ( ) ( )

1 2 3

, 0,

jack up jack up jack up jack up

S Leg Leg Leg Hull

t R t R t R t R t t

− − − −

=    R

(3)

where

( ) ( ) ( )

1 2 3

, ,

jack jack jack

Leg Leg Leg

R t R t R t

denote the

reliability functions of jack-up legs in jacking system

and

( )

Hull

denotes the hull’s reliability function.

Jack-up structure (Figure 3) with particular

emphasis on the jacking system can be divided into the

following main components [1], [21], [25]:

− Hull – buoyant, watertight structure that contains

ballast tanks and supports the legs, jacking system

and equipment (mostly drilling for O&G purposes

and Heavy Lift for Offshore Wind purposes). The

hull floats during transportation and can be jacked

up to elevate the rig above the water surface for

drilling or crane operations. The hull's strength is

crucial due to the high loads imposed by the legs

and jacking systems.

− Leg Structure – in terms of reliability structure – it

contains all parts (except the hull described above

that connects all legs) that can be assigned to each

leg individually:

− Jackhouse – machinery space on a jack-up

platform or vessel, housing the jacking system

that elevates and lowers the platform's hull

using movable legs (Figure 3). Jackhouse is from

one side welded to hull structure and from the

other connected to legs by rack chocks and/or

pinions (depending on the operation mode and

design).

− Legs – they support the hull when elevated,

providing stability under lateral loads. Two type

of legs are commonly used: trussed with triangle

or square shape and round – depending on the

jack-up design.

− Racks – critical components in a leg structure

with direct contact with pinions of jacking

gearbox as well as with yokes of rack chock

system. Legs depending on their type have

welded one or more racks.

− Rack chocks – components that provide a secure

mechanical lock, ensuring the platform's weight

is safely transferred to the legs during static

holding. The rack chock system operates

independently of the jacking system. This

separation allows the jacking pinions to be

unloaded or declutch once the hull is locked

with the rack chocks, increasing safety and

reducing wear on the jacking components. Most

of designs utilize them.

− Horizontal and Vertical Jacks – components for

moving and positioning rack chocks.

− Locking Mechanisms – self-locking mechanisms

that hold the rack chocks in position. This

mechanical locking minimizes or eliminates the

need for continuous hydraulic pressure to

maintain the locked position, increasing

reliability and safety even in the event of a

power loss. Variable solutions are available.

− Jacking Pinions – large gear wheels with teeth

that mesh precisely with the racks. These gears

are almost always seven-toothed, as this is the

fewest number of teeth that can be used to

achieve a contact ratio of >1. The rotating pinions

engage the rack teeth and convert rotational

motion into vertical movement, thereby raising

or lowering the hull relative to the legs.

Supported by heavy-duty bearings, the pinions

support the platform’s weight during jacking,

allowing for stable and controlled elevation or

lowering.

− Jacking Motors – low-speed and high-torque

hydraulic or electric motors with gearboxes

installed on jacking houses, used to lift or lower

the entire platform. The force is transferred via

jacking pinions.

− Spudcans – base structures welded to the lower

part of the leg structure that penetrates the

seabed. These are critical components for

ensuring stability during offshore operations

and are, in most cases, designed for installation

on the seabed.

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Figure 3. Side view of three-legged jack-up platform with the

jacking house marked in the frame (based on [33]).

To better illustrate the jacking system’s

construction, described above components are show in

exemplary representative scheme in Figure 4, from

actual design project that can be found on one of jack-

up platforms in the Baltic Sea.

Figure 4. Schematic view of a jacking system (based on [37]).

Legend: 1 – Chord Rack; 2 – Teeth; 3 – Jacking System; 4 –

Pinion; 5 – Elevating Jack Drive Motor; 6 – Deck Level; 7 –

Leg Well in Hull; 8 – Rack Chock System; 9 – Rack Chock

Assembly; 10 – Chock; 11 – Horizontal Screw Jack; 12 – Teeth

match with Chock; 13 – Upper Vertical Screw Jack; 14 –

Lower Vertical Screw Jack

The above scheme of a jacking system shows a view

of one rack of the jack-up leg. In the example

considered, a triangular-shaped trussed leg with three

double-sided rack and pinion subsystems was

designed. In that configuration, each leg has twelve

pinions that support the pontoon's weight during

jacking operations, including holding the preload,

which can result in approximately 60% greater load per

pinion than during a normal jacking. Six rack chocks

per leg hold the pontoon's weight during platform

operation.

2.2 Jack-up unit operations

Jack-up type vessels are highly versatile mobile

offshore platforms that serve multiple critical purposes

across various industries, particularly in the energy,

marine construction, and offshore sectors [3], [7], [13].

These self-elevating platforms have become

indispensable tools for operations in shallow waters

where stability and accessibility are paramount. To

properly describe and estimate reliability of jack-up

unit, basic operations, that are characteristic for this

type of units, have to be characterized [10]:

− transit – during this operation, legs are elevated

above the pontoon with spud-cans positioned close

to the pontoon, and rack-chocks secure legs against

movement. There are two types of towing: wet and

dry towing for units without propulsion, illustrated

in Figure 5.

− jacking – during this operation, the rack-chock

system is disengaged and the entire load rests on

pinions. In this state, the platform can be transited

from the afloat to the elevated position and from the

elevated to the afloat position. This is the most

critical operation, associated with numerous risks.

− elevated position – in this position, the spud-cans

stand on the seabed and the rack-chock system is

engaged transferring the entire load bypassing

jacking system.

Figure 5. (a) Wet towing of Lotos Petrobaltic (photo J.

Bogucki) [38], (b) Dry towing of Lotos Petrobaltic [39].

Depending on the operations performed, the

contribution and fatigue of the components, listed in

Subsection 2.1, during jack-up platform’s operation

may vary. Thus, taking into account the reliability

structure of jack-up platform, the following four modes

have been distinguished for consistency in the analysis:

− jacking mode – includes components active during

the elevating or lowering of platform,

− wet towing mode – includes components active

during the towing in buoyancy condition – see

Figure 5a,

− dry towing mode – includes components active

during the towing on barge – see Figure 5b,

− operation mode – includes components that are

active during operation, i.e. in the elevated position.

In our research, we point out that the reliability

structure of a jack-up platform depends on its

operating condition. Consequently, the reliability

function of a jack-up unit regarding different modes

takes the form:

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( )

, 0,

jacking

WetT

jack up jacking WetT DryT

jack up jack up

DryT Oper

Oper

jack up jack up

S M M M

t P T t P T t P T

t P T t t

−

−−

=  +  + 

+  

R R R

(4)

where:

P(TMjacking) – probability of jack-up platform jacking

mode,

P(TMWetT) – probability of jack-up platform wet towing

mode,

P(TMDryT) – probability of jack-up platform dry towing

mode,

P(TMOper) – probability of jack-up platform operation

(elevated) mode,

and

( ) ( ) ( ) ( )

, , ,

jacking DryT Oper

WetT

jack up jack up jack up jack up

M M M

S S S S

tttt

− − − −

R R R R

denote

reliability function of a jack-up unit in the jacking

mode, wet towing mode, dry towing mode and

operation mode, respectively.

In the remainder of this paper, based on the

knowledge of experts and platform operators, we

determine the aforementioned probabilities of the

platform's being in specific operational modes. In

further research analysis, we plan to conduct a detailed

analysis of the system's operation process, including

the realizations of transition times between operational

states and a detailed assessment of impact factors.

2.3 Multi-state approach to platform reliability

Analyzing the moment when a certain level is

exceeded, above which system operation may be

dangerous and pose a threat to people and the

environment, instead of determining only the time to

system failure, may be important from the practical

perspective in platform reliability analysis. Therefore,

in this paper, we propose a multi-state approach to the

reliability analysis [6], [8], [14], [23] of platform

structures, distinguishing reliability states s0, s1, s2, … si,

…, sN related to the platform’s condition, e.g.,

corrosion, age, wear, fatigue. Accordingly, we

distinguish several reliability states of the platform

and, from among them, we identify the state above

which further operation of the platform may be

dangerous. This approach can also be used to

determine the state, exceeding which indicates the

need for maintenance and repair. In further reliability

analysis in this paper, we distinguish the following

four reliability states for a jack-up unit:

− s0- unit failure state, the system cannot be operated,

− s1- critical system state, the system should not be

used due to corrosion, material fatigue or other

factors, as its operation may pose a threat to the

environment and/or the life and health of people

operating the system,

− s2- system reliability state indicating partial wear,

fatigue, corrosion or other factors, but enabling safe

operation of the system,

− s3- system full reliability state.

In this approach, the reliability function of multi-

state jack-up unit is defined by the vector [6], [23], [24]:

( )

jack up

−

=R

( )

( ) ( )

( )

0 1 2 3

, , , , , , , , 0,

jack up jack up jack up jack up

S S S S

t s t s t s t s t

− − − −







R R R R

(5)

where its coordinates are defined as the probability

that the time until the system exceeds fixed conditions

is not less than t, that is:

( ) ( )

( )

, , 0,1,2,3

jack up jack up

S i S i

t s P s t i

−−

=  =RT

, (6)

where TSjack-up(si) is a random variable representing the

time until the unit exceeds the conditions defined by si

state and the associated safety level of the offshore

structure.

Furthermore, considering the reliability structure

presented in Figure 2 and formula (3), the multi-state

reliability function of the jack-up unit takes form of the

vector:

( )

jack up

−

= R

( ) ( )

( )

1 2 3

1, , , , , , , 0,

jack up jack up jack up

S S S

t s t s t s t

− − −







R R R

(7)

where its coordinates are given by:

( )

( ) ( ) ( ) ( )

1 2 3

, , , , 1,2,3

jack up

jack up jack up jack up

Leg i Leg i Leg i Hull

R t s R t s R t s R t i

−

− − −

   =

(8)

where

( ) ( ) ( )

1 2 3

, , , , ,

jack jack jack

Leg i Leg i Leg i

R t s R t s R t s

denote

the reliability function coordinates of the jack-up

system leg. With these notations, the reliability

function coordinate

( )

jack

Leg i

R t s

is defined as the

probability that single jack-up system leg is in the

reliability state si or better in terms of reliability at time

During the design phase, it is assumed that all three

legs in a jacking system have the same reliability

parameters and reliability function. Therefore, in this

section, for notational simplicity, we consider the

reliability structure of jack-up system under this

assumption and determine the reliability function of a

single leg in the jack-up system.

In that case, formula (8) for the reliability function

coordinates of jack-up system structure, assuming the

identical structure of jack-up system leg, takes the

form:

( ) ( ) ( )

, , , 0, 1,2,3,

jack up jack up

S i Leg i Hull

t s R t s R t t i

−−



=   =



(9)

where

( )

jack

Leg i

R t s

denotes the reliability function

coordinate of single leg jacking system for the

reliability state si, i=1,2,3. In further analysis, taking into

account the operation history of the jack-up platform

and its influence on the platform reliability, we

consider the possibility of different reliability

structures of jack-up legs in different operating modes

of jack-up unit and the possibility of differential impact

on individual platform legs. Therefore, in Section 3, we

consider the jack-up platform as a heterogeneous

system and conduct the reliability analysis of each

platform leg separately.

3 TOWING AND JACKING HISTORY AND ITS

IMPACT ON JACK-UP PLATFORM RELIABILITY

Jack-up platforms experience damage accumulation

due to fluctuating loads, leading to fatigue failure

1394

when damage exceeds critical levels. Environmental

conditions, including wind and wave forces, contribute

to structural fatigue and can exacerbate degradation

[2], [31], [34], [35]. The reliability of jacking systems

must consider time-dependent factors, such as

corrosion and material degradation, which affect the

structural resistance over time [12], [32]. Advanced

reliability assessment methods, including Monte Carlo

simulations, can predict failure probabilities by taking

into account uncertainty in loading and material

characteristics [10], [20]. The mobility of jack-up

platforms requires the ability to adapt to changing

operating conditions, which can lead to increased wear

and potential failure modes. Regular inspections and

maintenance are crucial to assessing the remaining

fatigue strength and ensuring the reliability of the

platform throughout its operational life. As an

example, Table 1 presents factors that can affect the

platform reliability in jacking mode (from highest to

lowest).

Table 1. Selected factors influencing the platform reliability

in jacking mode.

Impact Factor Q1

Jacking system mechanical condition factor

Impact Factor Q2

Foundation and soil interaction factor

Impact Factor Q3

Load distribution and structural response factor

Impact Factor Q4

Operational control factor

Each operating mode contributes unique damage

patterns to the overall structural integrity. According

to research results and literature, different operating

modes activate distinct failure mechanisms:

− Jacking Mode – concentrates mechanical stress on

the jacking system components, with the rack-

pinion interfaces experiencing peak load

conditions.

− Operation Mode – subjects leg structures to cyclic

environmental loading, following traditional

fatigue models for offshore platforms.

− Towing Modes – introduce dynamic loading

conditions not occurring in stationary operations,

with quite a significant impact from hull-leg

interactions near spudcan [29], [30].

There are many influence factors that vary for each

operating mode. For example, the Jacking System

Mechanical Condition Factor (hereinafter referred to as

the impact factor Q1 for jacking operations) is a

dimensionless parameter that quantifies the

mechanical health and performance degradation of the

jacking system during jack-up platform operations.

The calculation begins with an assessment of the

individual mechanical components of the jacking

system, taking into account load-dependent factors

based on the operating conditions, wear and

degradation assessment, and the Weibull distribution

for component reliability.

The fatigue life of a jack-up structure, including the

jacking system, depends on operational strategy which

determines, for example, the frequency and conditions

of towing (dry or wet towing type). Therefore,

considering the influence of jacking, operation, and

towing history, is necessary for accurately assessing

the reliability and lifetime of aging platforms. The main

thesis of this paper is that jacking and towing

operations have a measurable, cumulative impact on

platform reliability, which must be incorporated into

modern assessment methodologies.

3.1 Fatigue damage process

Jack-up platforms are designed to operate in transit,

preloading, and operational conditions, all of which

can contribute to fatigue damage [29]. Fatigue analysis

of offshore structures is often based on S-N data as

recommended for example by DNV document on

fatigue design of offshore steel structures practices [11].

The guideline indicates that in fatigue analysis nominal

S-N curves can be applied, however in case of

exceeding the inherent S-N data in fabrication

tolerances, additional stress analysis for butt welds and

cruciform joints is required. Finite Element Models

(FEM) are often used to conduct dynamic analysis in

the time domain, and the Palmgren-Miner rule, also

known as Miner's linear cumulative damage rule, is

applied in engineering to estimate the fatigue damage

of structures subjected to variable amplitude stress

cycles. It is particularly relevant for offshore structures

like jack-up platforms, which experience fluctuating

stresses due to environmental loads such as waves,

wind, and currents [29], [30].

The Palmgren-Miner rule assumes that fatigue

damage accumulates linearly with each stress cycle,

irrespective of the loading sequence. The fatigue

damage D is calculated as the sum of the ratios of

applied stress cycles to the number of cycles to failure

at a given stress level:



(10)

where B denotes number of stress blocks and the total

stress range spectrum is discretized into a certain

number of blocks.

The fatigue damage of the b-th stress block is given

by:

(11)

where nb is the number of stress cycles occurring in the

stress range Sb, and Nb is the number of cycles to failure

in the stress range Sb, determined from the material's S-

N curve.

Despite its widespread use in engineering design

[15], [29], [30], [36], Miner’s rule has several key

limitations that the authors are aware of, such as the

lack of load sequence effect, linear damage summation,

ignoring the mean stress and environmental influence,

scatter and statistical variability, and limited

applicability to constant‐amplitude S-N data [5], [17],

[27].

In this paper, we focus on the primary fatigue data

of offshore structure based on S-N data for reliability

analysis. Nevertheless, due to the specific nature of

jack-up platform operations and the influence of

towing and jacking operations on the actual structure

state, the history of structure's operation is included in

its reliability analysis. Thus, we propose to apply a

multi-state approach and determine the reliability

function of offshore structure, taking into account the

operation process of jack-up platform. We consider the

influence of towing and jacking history on the jack-up

structure reliability, based on the fatigue damage ratio

1395

introduced by the Palmgren-Miner rule. We assume

that the impact factors can take different values for

different reliability states si, i=1,2,3, and operating

modes i.e. jacking mode, wet towing mode, operation

mode and dry towing mode. Additionally, we assume

that the operating history may deteriorate the

component condition more than expected. However,

due to natural fatigue and other factors, such as

corrosion, the reliability parameters cannot be better

than designed. With these assumptions, we propose

the impact factor of jacking history on platform

reliability in the following basic form:

( )

, ,1 , 1,2,3,

jacking

N T s

Q T s min i

n T s











(12)

where

( )

N T s

is the number of operations

designed for the offshore structure component, being

in a reliability state si, in the jacking mode during

operational time T, and

( )

n T s

denotes the number

of operations carried out in the jacking mode during

operational time T, in which the offshore structure

component was in the reliability state si.

Similarly, the influence of the platform's

operational history in other operating modes on the

conditional reliability function coordinates of jack-up

platform in particular modes is considered. That way,

the impact factors of operation history in wet towing,

dry towing and operation modes are proposed and

included in the further reliability analysis.

The number of permissible jacking up and down

cycles during the design life of a jack-up platform or

vessel is not universally fixed but depends on the

design criteria, operational profile, and fatigue factors

specific to each unit. Jack-up platforms are typically

designed for a service life of 25 years, during which the

jacking system - including the pinions, racks, and

structural components - is expected to perform reliably

under repeated jacking operations. The jacking system

and leg structures are subject to fatigue from cyclic

loading resulting from jacking operations,

environmental forces, and operational conditions. The

number of jacking cycles is limited by a fatigue life

assessment that takes into account the stresses during

jacking up/down and the dynamic environment.

Some design parameters for the jack-up unit of drill

type, analyzed in this paper, are given in Table 2. These

parameters, which relate to the actual wear rate of a

platform, can be used as a basis for estimating the

operational history impact factor.

Table 2. Selected design parameters of conventional full size

jack-up drilling unit.

Design number of jacking on site cycles per year

(typical)

Around 10

Assumed number of preload and level cycles per

jacking (typical)

Jacking time in 20 years of exploitation (estimation)

Around 320

hours

In a more advanced version, we can consider

various type factors in each operational mode, for

example those indicated in Table 1, influencing the

reliability parameters of components. In such a case,

these factors Q1, Q2, …, Ql, , l∈N, are considered with

coefficient weights w1, w2, …, wl, satisfying the

condition



. Taking into account the multi-state

approach to reliability analysis, proposed in this paper,

these factors can take different values for various

reliability states si, i=1,2,3. Under such assumptions, the

factor of influence on the jack-up unit reliability in any

mode can be given by the following formula:

( ) ( ) ( ) ( )

 

1 1 2 2

, , , , ,1 , 1,2,3

Mode Mode Mode Mode

i i i l l i

Q T s min w Q T s w Q T s w Q T s i=  +  + +  =

. (13)

The maximum value of impact factor can be 1, since

we assume that the reliability of offshore unit cannot

be better than it was designed for. Next, the

coordinates of the jack-up platform reliability function

are multiplied by these factors to take into account the

negative impact of the operation history on offshore

structure reliability. In particular, for a jack-up unit in

jacking mode, regarding the four factors listed in Table

1, formula (13) can be transformed as follows:

( ) ( ) ( ) ( ) ( )

 

1 1 2 2 3 3 4 4

, , , , , ,1

jacking jacking jacking jacking jacking

M M M M M

i i i i i

Q T s min w Q T s w Q T s w Q T s w Q T s=  +  +  + 

i=1,2,3, (14)

where the factor

( )

jacking

Q T s

can be estimated from

formula (12).

3.2 Impact of operation history on offshore structure

reliability

This paper presents a modified approach to platform

reliability analysis, taking into account its operational

history, unlike most papers that consider only the

system structure and design parameters. Since this

paper is the first stage of this research, we have

adopted impact factor values based on expert opinion.

In our future research, we plan to consider the

operating process and history of jack-up platform in

details, taking into account the number of operations of

a given type, their duration, external conditions

(including geological and environmental conditions),

and operational frequency characteristics, to determine

their impact on the actual fatigue level and reliability

of the jack-up unit. The purpose of this article is to

illustrate and highlight how considering the platform's

operational history can impact the reliability of the

entire unit and can be crucial for the safe operation of

the jack-up unit.

Moreover, when analyzing the operating process of

the jack-up unit, experts and operators have paid

attention to the possibility of uneven fatigue and

reliability level of each platform leg during operation.

For example, in practice, the bow leg may be more

loaded and subject to greater stress. and therefore, over

time, have lower reliability parameters than the stern

legs, due to geological conditions and related

foundation of the unit and the depth of the platform

legs. For that reason, we propose to consider three

different impact factors, based on formula (10) or (11),

which can take different values for each leg of the

platform, i.e.

( )

jacking

jack up

Leg

Q T s

−

( )

jacking

jack up

Leg

Q T s

−

( )

jacking

jack up

Leg

Q T s

−

. Similarly, we can distinguish the

impact factors of each leg on platform in other

operating modes, i.e.

( )

WetT

jack up

Leg

Q T s

−

( )

WetT

jack up

Leg

Q T s

−

( )

WetT

jack up

Leg

Q T s

−

for wet towing mode, and in further

analysis for dry towing mode and operation mode.

The reliability function coordinates of the jack-up

system structure in jacking mode, taking into account

different reliability states si, i=1,2,3, and the impact of

1396

jacking history on its reliability, can be determined

from the formula:

( ) ( ) ( ) ( )

, , , ,

, , , , 0, 1,2,3.

jacking jacking

jack up jack up

jacking

jacking jacking

jack up jack up

jack up

S i i Leg i i

Leg Leg

Leg i i Leg i Hull

Leg

t s Q T s R t s Q T s

R t s Q T s R t s R t t i

−−

−

=   

    =

(15)

Figure 6. The reliability function coordinates of the jack-up

unit in jacking mode, with and without the impact of

operation history.

Figure 6 illustrates the influence of jacking history

on the reliability of jack-up platform compared to the

results without this influence. In this paper, the impact

of the operating history is assumed to be relatively

small with respect to the design fatigue limits, and the

impact factor

( )

, ,

jacking

Q T s

i = 1, 2, 3, ranges from 0.94

to 1, where value 1 means no negative impact of the

jacking history and loading on the system beyond the

design limit. For other operating modes, the influence

factors range from 0.96 to 1.

Similarly, the reliability function coordinates of the

jack-up system structure in wet towing mode, taking

into account different reliability states si, i=1,2,3, and

the impact of towing history on its reliability, are given

by:

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

, , , , ,

, , , , 0, 1,2,3,

WetT WetT

WetT WetT WetT

jack up jack up jack up

jack up jack up

WetT WetT

jack up

M M M

S i i Leg i i Leg i

Leg Leg

i Leg i i Hull

Leg Hull

t s Q T s R t s Q T s R t s

Q T s R t s Q T s R t t i

− − −

−−

−

=    

    =

(16)

and during operation mode and dry towing mode,

respectively:

( ) ( ) ( ) ( ) ( )

( ) ( ) ( )

, , , , ,

, , , 0, 1,2,3,

DryT DryT

DryT DryT DryT

jack up jack up jack up

jack up jack up

DryT

jack up

M M M

S i i Leg i i Leg i

Leg Leg

i Leg i Hull

Leg

t s Q T s R t s Q T s R t s

Q T s R t s R t t i

− − −

−−

−

=    

   =

(17)

( ) ( ) ( ) ( ) ( )

( ) ( ) ( )

, , , , ,

, , , 0, 1,2,3.

Oper Oper

Oper Oper Oper

jack up jack up jack up

jack up jack up

Oper

jack up

M M M

S i i Leg i i Leg i

Leg Leg

i Leg i Hull

Leg

t s Q T s R t s Q T s R t s

Q T s R t s R t t i

− − −

−−

−

=    

   =

(18)

The graphs of reliability function coordinates of the

jack-up unit during wet towing, dry towing and

operation modes, based on formulae (16)-(18), are

shown in Figures 7, 8 and 9, respectively.

Figure 7. The reliability function coordinates of the jack-up

unit in wet towing mode, with and without the impact of

operation history.

Figure 8. The reliability function coordinates of the jack-up

unit in dry towing mode, with and without the impact of

operation history.

Figure 9. The reliability function coordinates of the jack-up

unit in operation mode, with and without the impact of

operation history.

Taking into account the operation history and its

impact factors, including jacking and towing

1397

operations, the reliability function of jack-up unit,

based on formula (7) and assuming multi-state

approach to platform reliability analysis, is given by

the vector:

( ) ( ) ( )

( )

1 2 3

, 1, , , , , , , 0,

jack up jack up jack up jack up

S S S S

t t s t s t s t

− − − −



 = 



R R R R

(19)

where its coordinates, considering the platform

operation process, can be determined from the

following formula:

( )

, , ,

, , , 1,2,3,

jacking

WetT

jack up jacking jack up WetT jack up

DryT Oper

DryT jack up Oper jack up

S i M S i M S i

M S i M S i

t s P T t s P T t s

P T t s P T t s i

− − −

−−

=  +  +

 +  =

R R R

(20)

and conditional reliability function coordinates in

particular operating modes are given by formulae (15)-

(18), respectively.

Figure 10 presents the coordinates of the

unconditional reliability function of the platform when

the operating history and its impact on the jack-up

platform reliability are taken into account, based on

formulae (20) and (15)-(18), and without taking into

account such influence.

Figure 10. The coordinates of the unconditional reliability

function of jack-up unit, taking into account the impact of its

operation history and without such influence.

The values of reliability function coordinates at the

moment t represent the probability that the time to

system exceeding certain reliability and safety

conditions is not less than t. Reversing this

relationship, by using the inverse function of the

coordinate, we can determine the moment when the

reliability function coordinate of jack-up unit exceeds

some fixed level, e.g. 0.8. Let’s denote:

( ) ( )

, , 0,

jack up

t t s t

−

=rR

(21)

and consequently by using its inverse function, if such

exists, we can determine the moment when the

probability of jack-up platform failure exceeds certain

level, from the following formula:

( )



−

= r

, where p∈〈0;1〉. (22)

Consequently, we can determine the moment when

the values of reliability function coordinates

( )

jack up

−

and

( )

jack up

−

fall below a certain level

p∈〈0;1〉 according to the formulae:

( )



−

= r

where

( ) ( )

, , 0,

jack up

t t s t

−

=rR

(23)

and

( )



−

= r

where

( )

, , 0.

jack up

t t s t

−

=rR

(24)

Tables 3, 4, 5 present the results of moments

1 2 3

, , ,

  

when the values of reliability function

coordinates

( )

jack up

−

( )

jack up

−

and

( )

jack up

−

, respectively, fall below a certain level p.

They are determined from formulae (22)-(24) for the

jack-up unit taking into account the impact of its

operating history on reliability. Similarly, the moments

1 2 3

, , ,

  

when the coordinates of unconditional

reliability function fall below a certain level p, for the

jack-up unit without taking into account such

influence, are determined and given in Tables 3, 4, 5,

respectively.

Table 3. Moments



and



of exceeding the probability

level by the coordinates of unconditional reliability function

of the jack-up unit.

Level of

probability p

Moments of exceeding the probability level p (in

years)



difference

0.9

7.9

4.0

49%

0.8

9.6

5.4

44%

0.7

10.6

6.6

38%

0.6

11.3

7.4

35%

0.5

12.0

8.1

33%

0.4

12.7

8.8

31%

Table 4. Moments



and



of exceeding the probability

level by the coordinates of unconditional reliability function

of the jack-up unit.

Level of

probability p

Moments of exceeding the probability level p (in

years)



difference

0.9

4.2

3.4

19%

0.8

5.6

4.3

23%

0.7

6.4

5.3

17%

0.6

7.1

6.0

15%

0.5

7.6

6.6

13%

0.4

8.2

7.1

13%

Table 5. Moments



and



of exceeding the probability

level by the coordinates of unconditional reliability function

of the jack-up unit.

Level of

probability p

Moments of exceeding the probability level p (in

years)



difference

0.9

1.4

0.8

1.9

0.7

2.2

2.1

0.6

2.4

2.3

0.5

2.6

0.4

2.8

2.7

Based on the results presented in this section, it can

be concluded that the most significant difference

occurs between the values of reliability function

coordinates

( )

jack up

−

, taking into account the

influence of platform’s operation history, and

( )

jack up

−

without such influence. This means that

the impact of operation history on the jack-up platform

reliability is crucial in the long term when comparing

the platform’s lifetimes, i.e. times of system being in the

reliability states s1, s2 or s3. Comparing the moments at

1398

which the reliability function coordinates exceed the

predefined probability levels (Tables 3, 4, 5),

corresponding to the time the system spends in the

reliability states s1, s2 or s3, the differences range from

approximately 30% to 50%. For the probability that the

platform is in the reliability states s2 or s3, the

differences between the moments of exceeding the

probability levels range from 13% to 23%, and for the

probability that the platform is in the reliability state s3

of full system reliability, these differences are

negligible (up to 5%). From these results, it can be

clearly shown that operational history has a

deterministic effect on the jack-up platform reliability,

and the scale of this effect is critically dependent on the

current degradation state of platform. For aged

platforms exhibiting degraded reliability states (s2 or s1)

– characterized by accumulated mechanical wear,

fatigue damage, or corrosion – the operational history

becomes a primary factor in determining reliability,

where additional operations beyond the original

design parameters or exposure to adverse operating

conditions can accelerate catastrophic reliability

degradation.

This phenomenon is revealed in the non-linear

relationship between cumulative damage and

operational stress, where platforms with pre-existing

degradation show increased sensitivity to changes in

operational history. In particular, when jack-up

platforms show partial wear of critical components

(jacking systems, structural connections, foundation

interfaces), fatigue crack propagation, or signs of

progressive corrosion, subsequent operating modes –

especially jacking operations, transit conditions, or

extended operational periods – can trigger accelerated

degradation mechanisms that fundamentally

compromise the platform’s integrity. The key finding

illustrates that the influence of operational history

follows a threshold-dependent model: platforms

maintaining a full reliability state (R ≥ 0.95) indicate

resilience to operational variations, with only a slight

degradation in reliability under unfavourable

conditions. In contrast, platforms in a state of reduced

reliability (R < 0.95) present exponential sensitivity to

operational history, where identical operational

sequences can yield significantly different reliability

results depending on the baseline level of platform

degradation. This threshold behaviour validates the

need for history-dependent reliability assessment

methodologies, as traditional approaches that assume

operational independence generally underestimate

failure probabilities for aged platforms while

potentially over-conservatizing assessments for

platforms in excellent condition. Thus, the operating

mode impact factor model provides the essential

analytical framework to distinguish platforms

requiring intensive historical evaluation from those

suitable for conventional reliability assessment

approaches.

4 CONCLUSIONS

The paper illustrates the relationship between

operating conditions and overall fatigue of a typical

jack-up structure in the context of the safety of future

operations. The results obtained show that operational

history has a significant impact on the reliability of a

jack-up structure. That can be crucial in lifetime

assessment and correction of estimated design lifetime.

Moreover, the detailed analysis of reliability of

individual legs and their fatigue is extremely

important, which from the point of view of operational

safety is more realistic and can provide a more

sustainable approach to maintenance and repairs –

which will be included as an additional impact factor

in our future studies. This multi-modal operational

framework represents a paradigm shift from

traditional static reliability analysis to dynamic,

history-dependent assessment methodologies. In our

future research, we plan to analyse the reliability

impact factors for each components depending on the

operating mode, as a multidisciplinary approach that

could help develop a supportive tool for lifetime

assessment of offshore structures.

ACKNOWLEDGMENTS

The paper presents the results developed in the scope of the

research project “Modeling, safety analysis and optimization

of critical infrastructure systems’ operation.”,

WN/2025/PZ/13, granted by GMU in 2025.

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